Chocolate Peppermint Cookies

1 cup all-purpose flour, plus more for surface
1/2 cup unsweetened Dutch-process cocoa powder
1/2 teaspoon baking soda
1/2 teaspoon baking powder
1/2 teaspoon salt
2 1/2 ounces (5 tablespoons) butter, softened
3/4 cup sugar
1 large egg
1 large egg yolk
3/4 teaspoon pure peppermint extract
8 large candy canes or 30 peppermint candies, crushed
2 pounds white chocolate or dark/milk chocolate, coarsely chopped

Preheat oven to 325 degrees. Whisk flour, cocoa powder, baking soda, baking powder, and salt in a bowl. In another bowl, beat butter and sugar with a mixer on medium-high speed for 1 minute. Reduce speed to medium-low, and add egg, then yolk, beating well after each addition. Beat in peppermint extract. Slowly add flour mixture, and beat until just incorporated. Shape dough into 2 disks, wrap each in plastic, and refrigerate until firm, at least 1 hour (or up to 2 days).

Roll out 1 disk of dough on a lightly floured surface to 1/8-inch thickness. Freeze until firm, about 15 minutes. Using a 2-inch round cutter, cut out circles, and place 1 inch apart on parchment-lined baking sheets. Roll and cut scraps once. Freeze cookies until firm, about 15 minutes. Repeat with remaining disk.

Bake until cookies are dry to the touch, about 12 minutes. Transfer parchment, with cookies, to wire racks, and let cool. (Undecorated cookies will keep, covered, for up to 3 days.)

Sift crushed candy, and separate larger pieces from dust, reserving both. Melt chocolate in a heatproof bowl in the microwave (don't overheat or the chocolate/almond bark will sieze!). Dunk cookies into melted chocolate. Using a fork, press lightly on the cookie until completely submerged in the chocolate. Pick up the cookie with the fork, let excess chocolate drip off, and gently scrape bottom against edge of bowl. Place on parchment-lined baking sheets, and sprinkle 1/4 teaspoon of either candy pieces or dust on top. Repeat, sprinkling half the cookies with pieces and the rest with dust. Refrigerate until set, up to 3 hours.